The Math Intensive Academic Network had another successful conference in Omaha.
Our team kicked off the conference with a Themed Session that included presentations from precalculus, calculus, linear algebra, and advanced mathematics. Thanks to presenters Lee Wayand, Keith Nabb, Mike Caparula, and Amber Severson for sharing their insightful innovations and valuable experiences, and appreciation to the fifty plus attendees who eagerly participated. Next year's themed session in Atlanta is titled, "Balancing Technology in Math Intensive Courses." Contact me at bob.cappetta@amatyc.org if you are interested in submitted a proposal for a fifteen-minute presentation
Our team next met on Friday afternoon for our yearly planning meeting. Our first goal is to finalize position statements. One concerns updating the precalculus curriculum to better serve current students and another concerns clarifying and promoting dual enrollment mathematics courses for high school students. Check our community page on my.amatyc.org for opportunities to share your thoughts on these issues.
Our second goal is to participate in the standards review process. Our team is charged with updating the Mathematics Intensive section of Chapter 6 in the Crossroads document. Please read the current chapter at https://my.amatyc.org/impactlive-home/standards-docs/beyond-chapt056 Comments may be shared on the discussion board for our community at my.amatyc.org. We plan to schedule virtual meetings to discuss these issues and more. Dates and times will be announced on my.amatyc.org.
Our third goal for the coming year is to increase opportunities throughout the year for communication and networking.
In an attempt to stimulate interaction, we are strongly encouraging members to post questions and comments about certain courses each month.
Consider sharing your concerns on comments on the discussion board/library on the Math Intensive Community page on my.amatyc.org.
December - Discrete Math
January - Linear Algebra
February - Multivariate Calculus
March - Sequences and Series
April - Integral Calculus
May - Differential Calculus
June - Trigonometry
July - Precalculus Algebra/College Algebra
Please visit our Library on the Math Intensive Community page on my.amatyc.org where you will be able to access presentation slides from previous conferences, and classroom materials that members have graciously shared. Please consider adding some of your favorite materials to that library collection.
The Math Intensive Academic Network finished the conference with a sharing session. Some highlights from the discussions follow.
The discrete math conversation focused on the challenges that students have with proof. Questions included whether or not the prerequisites were sufficient to foster the type of mathematical maturity needed for success in the course. Another was whether or not the principle of mathematical induction should be taught in the precalculus curriculum. Participants spoke highly of Miriam Harris-Botzum's presentation titled, "Puzzling Through Discrete Mathematics." Her slides are available in the library section of the mathematics intensive community page.
The linear algebra conversation focused on what the course should be. Must it be designed for future mathematics majors or future computer science majors? Some universities want a proof-based class and others want a matrix algebra class, so it is difficult to design one class that will transfer everywhere. If universities require a third-year course that is equivalent to a community college course, how can this transfer difficulty be overcome? Furthermore, prerequisites vary from school to school and many students seem insufficiently prepared. The OER book, "Understanding Linear Algebra" by David Austin was recommended.
The multivariate calculus discussion focused on the emerging technology that can be used to help students visualize concepts. Paul Seeburger's Calc3D Plot has been a favorite for years. New tools from Desmos and laser-printed 3D models provide additional opportunities. Another topic of discussion was the role of vector calculus. It seemed that most participants were able to spend sufficient time on these topics. Those that were not able to do so, typically came from schools with fewer total semester hours for the calculus sequence. It is not clear what the standard number of semester/quarter hours should be for calculus. Many recognized that setting up integrals for vector calculus and then using technology to evaluate them may be an appropriate strategy.
The differential equations discussion focused on the future of this course. Traditional procedural problems are likely to be de-emphasized. One concern is that this might transform differential equations from a mathematics course to an engineering/physics course with an emphasis on modeling rather than problem solving. Might theoretical concepts like existence and uniqueness become more important? Might data be used to create models for differential equations? Are traditional numerical strategies less important with emerging technology?
The sequences and series discussion focused on the concepts that are studied. Most participants included all of the traditional tests of convergence. The concern was that students do not really know what convergence means. Using technology to plot partial sums was suggested as an aid in understanding.
The integral calculus discussion focused on the integral techniques used and the types of application problems studied. Again it seemed that all of the traditional techniques were still being studied. One question is whether integral tables are still being used. There was some concern about the type of applications. Volumes of solids, and work were still emphasized. Separable differential equations like Newton's Law of Cooling and logistic models were thought to be important examples, however, new applications outside of engineering are needed. Might problems from bio-math, or economics/finance be more engaging for students?
The differential calculus discussion focused on under-prepared students. Algebra and trigonometry skills are lacking partially due to the challenges of learning during the pandemic. Another concern is the rush to calculus for dual enrollment students. Geometry seems especially weak for many of them. Are we doing a disservice to rush students to calculus before they are ready to succeed?
The precalculus discussion focused on to what degree these courses prepare students for calculus. It was generally thought that re-design with a focus on calculus would be preferable. Traditional topics like polynomial theory are less important due to technology. Developing function sense must be the primary goal. Lee Wayand is leading such an effort and I encourage interested people to examine his presentation slides and his OER book.
We are an extremely active community with many important challenges. Please consider joining our team and participating in the process